I'm having trouble applying contrapositives because in many instances they seem like bunk. Specifically, it seems like they require unsupported assumptions other than those that can be derived from game rules. Here is an example:

A group of three must be selected from the variables, A, B, C, D, & E:

1. If C is not selected, then B is not selected

2. D and E cannot both be selected

3. In order for A to be selected, B must be selected.

According to the study guide that I'm using, the contrapositive of rule 1 is, if B -> C. As I see it, although B -> C may be true there is nothing that requires it to be true. To my mind and contrary to the contrapositive of rule 1, it is also possible, although not required under the rules that if B is selected then C is still not selected. That being said, contrapositives are a proven concept and its unlikely that I'm right and my study book is wrong, so what am I missing, what systematic leap in logic am missing to make the concept of contrapositives useful on the LSAT? Thanks